# Why is (+1) x (-1) = (-1) ?

Discussion in 'Mathematics and Physics' started by neptune, Jan 6, 2012.

1. ### neptuneMember

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In reality i have forgotten basic Maths , so can any body remind me

+1 x +1 = +1
But -1 x -1= +1 why ?

Thankyou

2. ### ronsimpsonWell-Known MemberMost Helpful Member

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+1 x +1 = +1
(+1) x (-1) = (-1) The x(-1) causes the first number to change sign. from + to - (+5) x (-1) = (-5)
-1 x -1= +1 Same as above. The first -1 changes sign, from -1 to +1.

3. ### neptuneMember

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what is the logic behind it ? you know when we do minus we move left of no. line and when we add something we move right on no. line , so what do minus minus do to become positive and move right on no. line

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5. ### DerStrom8Super ModeratorMost Helpful Member

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+1 times x is always x. -1 times x means the opposite of (1 times x). Therefore, -1 x 1 = the opposite of 1x1 = -1. -1 x -1 = opposite of 1x-1 = 1.

Hope you can follow my logic there

You're talking about addition and subtraction. Keep in mind that this is multiplication, so moving left or right on the number line doesn't help much. - and + in this case are signs, not addition or subtraction.

Last edited: Jan 6, 2012
6. ### MrAlWell-Known MemberMost Helpful Member

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Hi,

The most basic operation is that of counting objects. We count 1, +1 more, +1 more, finding a way to identify groups that contain more than one object and call them something else so we can recognize them more quickly 1,2,3,... .

Multiplication is just an extension of counting. If we have 2*3 we are counting 3 objects two times, or counting 2 objects 3 times.

The invention of negative numbers allows us to count in two directions which are opposite to each other. If we count 3 objects to the right and 1 object to the left, we have 3-1 which of course brings us to the second (2) object. So if we have 2*(-3) we are counting three objects in the opposite direction (of normal) twice, or we are counting 2 objects three times in the opposite direction. The result is 6 objects in the opposite direction (of normal).

So if right is normal, if we have (-2)*(-3) then we are counting three objects oriented left two times oriented in the opposite direction, which means we end up counting right (with right being the normal direction).

The rule for two signs in tabular form of course is:
-- = +
+- = -
-+ = -
++ = +

Another interesting question, can we really have zero of something? If we have zero of something, then we already dont have anything to have zero of it of

Last edited: Jan 6, 2012
7. ### neptuneMember

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So just Because we dont consider + right direction and - left direction we are left with this dillema. we consider here + normal and - as going in opposite of whatever direction we were coming from. Did I got this right ?
what do you mean ?

8. ### MrAlWell-Known MemberMost Helpful Member

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Hi,

Yes multiplication is a form of addition, and addition is a form of counting, so multiplication is a form of counting too.

Yes left and right or one way and opposite way is important. We get into more directions later.

It's interesting that if we have zero of something that we have to specify what that something (that we dont have any of) is. That's strange if you think about it. We cant have zero of anything unless we say what it is we dont have. If i say "i have zero" that doesnt mean anything, unless i also say what it is i dont have, such as "i have zero pencils", "i have zero flowers", etc. This is more comparative then anything else, as person A can have 10 pencils but person B can have zero pencils, so one person has more than the other.
Might also raise the question is there such a thing as nothing at all anywhere in the universe.

9. ### neptuneMember

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if i say "i have one" that also doesnt mean anything, we have to specify unit or whatever we were counting.
And what are you counting in Universe ? you should specify it.

10. ### DerStrom8Super ModeratorMost Helpful Member

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If there is something that doesn't exist in this universe, then we have not defined it. Therefore, we cannot say we have 0, because we do not know the unit.

However, I can say I have zero mugs in my hand, which is true. I am not holding a mug. However, since a mug exists, I can certainly say I have zero right now.

11. ### GrosselMember

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Hi.

Think about this: You're looking into a mirror and looking at yourself. Say that the distance between mirror's surface and you is 2 meters (or whatever unit, insert what feels right). Call this distance "A".
Then we define the distance between mirror surface and your reflection "B". This distance will be measured in reverse direction, that is below zeero.
That means, if A = 2 meters then B = (-1)* 2 meters = -2 meters.

Even more important is this to understand when talking about power transmission. If current shifts phase, that means that effekt floats in reverse direction (or could be capasitive load goes inductive).

So there is houndreds ow ways to explain logical why (-1) makes sign to shift.

And since it's very popular to compare electric to water pipes, I will do that too.
Say you have two chambers with a pipe between. Both chambers is under certain pressure. Let's call the chambers A and B. A is always reference and is 0. All pressure is positive.
If chamber B has a higher pressure than A (positive number), then the water will flow from B to A, wich we define as positive direction. Let's say we meassure it as liter's pr second.
However, if chamber B has a negative pressure (pressure in A is higher), then is't pretty obvious that the water will flow in opposite direction, right? And oposite direction then must be a negative number.

If thinking about it, negative numbers give almost perfect sense.

In some few cases, negative numbers cannot be used. Typical cases is areas and volumes. Even both areas and volumes can be subtracted from each other, I can't see nowhere that a negative area or negative space should exists. (í in imaginary numbers is an exeption, but it's not actual real)

Last edited: Jan 9, 2012
12. ### 3v0Coop Build CoordinatorForum Supporter

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It would be wrong to say "no such thing as empty space" implies that there is no such thing as zero or having zero of anything.

Last edited: Jan 9, 2012
13. ### neptuneMember

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@Grossel
your explaination is bad ! contradicting itself.. what MrAI has said is right +ve is normal doesnt matter which direction and -ve is going in opposite direction on what was normal doesnt matter in which direction.
On a seperate account, can any body give me Real world Examples of using this rule (-)*(+)=(-) or (-)*(-)=(+)?

14. ### neptuneMember

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nothing can go Zero in this universe..Time has already started Ticking after Big Bang. what we have defined is singularity i.e. 1 at some places , but nowhere in universe everything is Zero

15. ### 3v0Coop Build CoordinatorForum Supporter

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Sure think of speed*direction, traveling from A to B as moving in the + direction and from B to A as traveling in the - direction. Multiplying by a - indicates that you reverse the direction of travel. A (-)*(-) has no net effect on the direction which is an illustration of (-)*(-)=(+).

Zero exists int the world of integers. How many pets does a person have? How many homes does he own. Zero is one possible answer for all of these questions.

16. ### GrosselMember

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Talking about positions in the univers isn't exactly basic math, is it?

Because most object's in universe isn't pure mathematical objects, and therefore basic math will not always apply.

In that case, you might be in war against laws of math and physics.
I tried to give an example, and you refused it without stating why. Don't you have any education in basic physics?

Last edited: Jan 10, 2012
17. ### neptuneMember

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Any Natural phenomena you can think of i.e. in Electronics..

18. ### 3v0Coop Build CoordinatorForum Supporter

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My example was natural.

In electronics we have inverting amps. Two inverting amps with unity gain illustrate how two -'s make a +.

19. ### Mr RBWell-Known Member

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I always knew that 2 wrongs make a right...

Ancient proverb writers sucked at math, they probably took philosophy at Uni because they didn't have the math grade.

20. ### 3v0Coop Build CoordinatorForum Supporter

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And 3 rights make a left.

Last edited: Jan 10, 2012
21. ### tytowerBanned

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Actually I fit that but I went to Accounting and Law
Accountants only add up columns of money and the worst is working out compound interest but we use an easy "Rule of 78"
Solicitors its even easier , we forget anything under \$1000
Liquidators , everything belongs to someone else so why worry - just guess